NONLINEAR ROLL MOTION OF SHIPS USING AKBARI-GANJI METHOD

Abstract

The non-linear second-order differential equation of roll motion of ships is comprised of three main components, namely the inertia forces and moments, restoring forces and moments, and damping forces and moments. In this paper, analytical expressions of roll angle in terms of time for linear-plus-quadratic damping and linear-plus-cubic damping roll motion of ships are presented using Akbari-Ganji method. Also, roll velocity, restoring moment, and damping moment can be obtained. The analytical results are compared with the simulation results. A satisfactory agreement is noted.